Nurse Deb Davies finished her evening shift only few hours ago but is already cheerfully bounding up and down the staircases of the Greenwood flats in the Welsh city of Newport.

It takes her and her fellow Labour candidates for the Beechwood ward only 40 minutes to canvass the 70 flats in the block. As they walk away, two Vote Labour posters appear in windows. "It's always a good sign when you look back at where you've just been knocking on doors and the posters have been put up," says Davies. "We're optimistic we're going to have a really good election night."

Beechwood, north of the city centre and bisected by the M4, is held by three Liberal Democrats. The city council, once a Labour stronghold, is run by a Conservative-Lib Dem coalition. This is the sort of area and sort of city in which Labour needs to do well if it is to regain its position as the dominant political force in Wales.

Not surprisingly, the election leaflet that Davies and her colleagues have been delivering flags up both local and national issues. It claims that Beechwood people are telling them "things are hard" because of the "pensioner tax" and "millionaire tax cuts" introduced in the budget. It argues that "savage cuts" at Newport's passport office and a city centre "in decline" are exacerbating the problems. And it also focuses on the hyper-local: the dog poo, the off-road bikes causing havoc in the woods, the fly-tipping and graffiti.

Betty Glazier, a retired civil servant, greets them warmly. "I'm voting for you," she tells Davies. "My hand would fall off if I voted for anyone else. I've always voted Labour. It's sad that the Tories and Lib Dems got in here. Wales is a Labour sort of place and Newport is absolutely Labour. The other lot have wrecked this town. When I go into the town I am ashamed of the state of the place."

Nancy Cooke breaks off from her sewing to explain how she has fallen out of touch with close friends she made when the city council closed down the day centre she attended, to save money: "I miss going down there and I miss my pals." But she also says she is fed up with the number of election leaflets dropping on her doormat. "I've got them coming out of my ears: Tory, Lib Dem, Labour, independent. I'm not sure I'm keen on any of them."

Roger Williams, a care assistant and driver, says he used to vote Labour in the days of Neil Kinnock. "But I own a few shares and so I started voting Tory. However, I'm a bit disappointed in some of the things Cameron has done, like putting up VAT to 20%. That has made life more difficult."

Fierce campaigns are being waged across Wales four years on from a horrible election for Labour, when it lost control of heartland seats in places like Newport, other traditionally socialist cities and towns, and even in the south Wales valleys. This time it has high hopes of taking back control or making significant inroads in places such as Newport, Swansea and Wrexham, all run by the Liberal Democrats with others.

Launching Labour's campaign down the road from Beechwood on the banks of the river Usk, the shadow Welsh secretary, Peter Hain, revealed a two-pronged attack. Hain explicitly called on voters to make 3 May a "referendum" on the Westminster government's "unfair and disastrous" budget and its "savage and reckless cuts". But then he stepped back and let local activists – the editor of a community magazine in Newport, a young mother who helps run a community centre in Cardiff, a former policeman from the valleys – take centre stage to say why they would be voting Labour.

The party is not producing a national manifesto for 3 May but instead is encouraging local groups to draw together their own pledges tailored to their areas. The Welsh first minister, Carwyn Jones, who leads a minority Labour government at the Welsh assembly, said it was a new style of Labour campaign, with local people in charge: "We had a very bad year in 2008. We're working hard to put that right." Asked which results really hurt four years ago, Jones reeled off a pretty long list: "Newport, Swansea, Wrexham, Flintshire, Merthyr, Blaenau Gwent, Torfaen … There are others."

The Tories also chose Newport to launch their Welsh campaign, in a function room at the home of the rugby team Newport Gwent Dragons. They have produced a national manifesto, which includes promises to freeze council tax and abolish business tax for small businesses. However, the most eye-catching pledge is to freeze tolls on the M4 and M48 Severn bridges – it now costs a car driver £6 to enter Wales via the bridges. Other parties ridicule the pledge, pointing out that the tolls were set by the company that operates the bridge and confirmed by a parliamentary order at Westminster.

The Tories are fielding more candidates than ever but accept they are in for a tough time because of the national picture. The Tory leader of Newport city council, Matthew Evans, said there was "apathy" on the doorstep from the sort of people who might have voted for the party four years ago – which is the problem Labour had in 2008.

But it is the Liberal Democrats who may have most to lose in Wales. Labour is fighting hard to win in Cardiff, where the Lib Dems govern with Plaid Cymru, and it would be a bitter blow to Nick Clegg's party if the Welsh capital fell. The Lib Dem leader in Wales, Kirsty Williams, acknowledges it is a challenge to get voters to focus on the work of the party locally, when the national party is struggling.

Plaid Cymru, meanwhile, has a new young leader, Leanne Wood, and a set of interesting pledges, including providing more apprenticeships, helping more local businesses to secure public service contracts and introducing schemes to allow communities to benefit from the ownership and control of natural resources. The party is hoping it will be able to move on from its disappointing performance in the assembly elections, when it was overtaken by the Tories.

Back in Newport, Christina Cox, 18, is discussing politics with her friend, Kieran Morris, 29, in the city centre's John Frost Square, named after the 19th-century Chartist hero. Cox isn't certain how she will use her first vote. "I'm not sure any of them will help me get a job," she says. "I was in work-based training but lost that when I got a throat infection. I've been looking for work since February and can't get anything."

The square, which has been due for redevelopment for years, is looking a little shabby. "I'm not sure the council is doing much to improve the city centre," says Morris, an artist. "It doesn't feel like somewhere that is going places. I'm not sure who I should be voting for.

"But I will vote – I don't think you're entitled to complain about what is going on if you don't use your vote." And he vows to head off to the library later to do some research – "as long as they haven't shut it down yet."

In Wales the council seats being defended are:

The candidates are as follows:

• Labour 842

• Conservative 571

• Plaid 580

• Liberal Democrat 343

• Green 66

• Ukip 15

• Others 841

There will be elections in all but one of the 22 councils in Wales. There will be no elections on Anglesey until next year, following a critical report on how the island was being run by the auditor general for Wales.

The Welsh government is run by a minority Labour administration. Labour has 30 of the 60 seats while the Tories have 14, Plaid 11 and Lib Dems five. Labour is the biggest party in Newport. But the Tories and Liberal Democrats work together to rule. The Lib Dems are the biggest party on Cardiff council, with 34 seats. The Conservatives have 16, Labour 14 and Plaid six.

More than 2 million people will be eligible to vote in Wales. At the assembly elections last year, 2,289,735 people were registered to vote and 41.8% of them did. Overall, 17% of voters asked for a postal vote and a high proportion of those, 71%, used it.